code: def _getitem(self, row_index, col_index, *batch_indices):
      x1 = self.x1
      x2 = self.x2
      num_outs_per_in = self.kernel.num_outputs_per_input(x1, x2)
      if isinstance(num_outs_per_in, tuple):
          num_outs_per_in_rows, num_outs_per_in_cols = num_outs_per_in
      else:
          num_outs_per_in_rows = num_outs_per_in
          num_outs_per_in_cols = num_outs_per_in
  
      # We will be running the __getitem__ command on x1, x2, and the kernel parameters
      # Since kernels can broadcast, x1, x2, and the kernel parameters may not have all of the batch dimensions
      # that are being indexed by the __getitem__ operation
      # Therefore, we begin by figuring out the broadcasted shape, and expanding all of these objects to that shape
      try:
          batch_shape = torch.broadcast_shapes(
              x1.shape[:-2], x2.shape[:-2], self.kernel.batch_shape
          )
      except RuntimeError:
          raise RuntimeError(
              f"The kernel inputs (sizes {x1.shape} and {x2.shape}) are incompatible with the kernel "
              f"(batch size {self.kernel.batch_shape}). This is likely a bug in GPyTorch."
          )
  
      # The row index and col index should exactly correspond to which entries of x1 and x2 we need
      # So we'll basically call x1[*batch_indices, row_index, :], x2[*batch_indices, col_index, :]
  
      # However - if we have multiple outputs per input, then the indices won't directly
      # correspond to the entries of row/col. We'll have to do a little pre-processing
      if num_outs_per_in_rows != 1 or num_outs_per_in_cols != 1:
          if not isinstance(row_index, slice) or not isinstance(
              col_index, slice
          ):
              # It's too complicated to deal with tensor indices in this case - we'll use the super method
              return self.evaluate_kernel()._getitem(
                  row_index, col_index, *batch_indices
              )
  
          # Now we know that x1 and x2 are slices
          # Let's make sure that the slice dimensions perfectly correspond with the number of
          # outputs per input that we have
          row_start, row_end, row_step = (
              row_index.start or 0,
              row_index.stop or self.shape[-2],
              row_index.step,
          )
          col_start, col_end, col_step = (
              col_index.start or 0,
              col_index.stop or self.shape[-1],
              col_index.step,
          )
          if row_step is not None or col_step is not None:
              return self.evaluate_kernel()._getitem(
                  row_index, col_index, *batch_indices
              )
          if (
              (row_start % num_outs_per_in_rows)
              or (col_start % num_outs_per_in_cols)
              or (row_end % num_outs_per_in_rows)
              or (col_end % num_outs_per_in_cols)
          ):
              return self.evaluate_kernel()._getitem(
                  row_index, col_index, *batch_indices
              )
  
          # Otherwise - let's divide the slices by the number of outputs per input
          row_index = slice(
              row_start // num_outs_per_in_rows,
              row_end // num_outs_per_in_rows,
              None,
          )
          col_index = slice(
              col_start // num_outs_per_in_cols,
              col_end // num_outs_per_in_cols,
              None,
          )
  
      # Define the index we're using for the last index
      # If the last index corresponds to a batch, then we'll use the appropriate batch_index
      # Otherwise, we'll use the _noop_index
      if self.last_dim_is_batch:
          *batch_indices, dim_index = batch_indices
      else:
          dim_index = _noop_index
  
      # Get the indices of x1 and x2 that matter for the kernel
      # Call x1[*batch_indices, row_index, :]
      try:
          x1 = x1[(*batch_indices, row_index, dim_index)]
      # We're going to handle multi-batch indexing with a try-catch loop
      # This way - in the default case, we can avoid doing expansions of x1 which can be
      # costly in terms of time
      except IndexError:
          x1 = x1.expand(*batch_shape, *x1.shape[-2:])
          x1 = x1[(*batch_indices, row_index, dim_index)]
  
      # Call x2[*batch_indices, col_index, :]
      try:
          x2 = x2[(*batch_indices, col_index, dim_index)]
      # We're going to handle multi-batch indexing with a try-catch loop
      # This way - in the default case, we can avoid doing expansions of x2 which can be
      # costly in terms of time
      except IndexError:
          x2 = x2.expand(*batch_shape, *x2.shape[-2:])
          x2 = x2[(*batch_indices, col_index, dim_index)]
  
      if len(batch_indices) == 0 or all(
          ind == slice(None, None, None) for ind in batch_indices
      ):
          new_kernel = (
              self.kernel
          )  # Avoid unnecessary copying when we aren't explicitly indexing batch dims
      else:
          try:
              new_kernel = self.kernel.__getitem__(batch_indices)
          # We're going to handle multi-batch indexing with a try-catch loop
          # This way - in the default case, we can avoid doing expansions of self.kernel which can be
          # costly in terms of time
          except IndexError:
              expanded_kernel = self.kernel.expand_batch(batch_shape)
              new_kernel = expanded_kernel.__getitem__(batch_indices)
  
      # Now construct a kernel with those indices
      return self.__class__(
          x1,
          x2,
          kernel=new_kernel,
          last_dim_is_batch=self.last_dim_is_batch,
          **self.params,
      )
  
imports: import functools
  from typing import Callable
  import torch
  from linear_operator import LinearOperator, to_linear_operator
  from linear_operator.utils.getitem import _noop_index
  from ..None import beta_features, settings
  from ..utils import deprecation
  from ..utils.memoize import cached
label_desc: Use image node_id 9 for calling the LazyEvaluatedKernelTensor obj's underlying member method code with example usage: obj._getitem(row_index, col_index) and returns: self, self, self, self